Friday, August 14, 2009
RIP Les Paul
On August 13, 2009, my world (and yours too, whether you knew it or not) became a little less cool.
Thursday, August 13, 2009
Forty-Two
So I'm currently 42 years old. If you're a Douglas Adams fan, you will recognize "42" as the answer to The Ultimate Question of Life, the Universe, and Everything.
Here's a few clues as to why that is the case . . .
In Mathmatics
Forty-two is an Abundant Number; its factorization 2x3x7 makes it the second sphenic number and also the second of the form {2x3xr}. As with all numbers of this form, the aliquot sum is abundant by 12. Forty-two is also the second sphenic number to be bracketed by twin primes; 30 also rests between two primes. 42 has a 14 member aliquot sequence: 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0, and is itself part of the aliquot sequence commencing with the first sphenic number, 30.
Further, 42 is the 10th member of the 3-aliquot tree.
Forty-two is the product of the first three terms of Sylvester's Sequence; like the first four such numbers, it is a primary pseudoperfect number.
It is the sum of the totient function for the first eleven integers.
It is a Catalan Number. Consequently, 42 is the number of noncrossing partitions of a set of five elements, the number of triangulations of a heptagon, the number of rooted ordered binary trees with six leaves, and the number of ways in which five pairs of nested parentheses can be arranged.
It is the reciprocal of a Bernoulli Number.
It is conjectured to be the scaling factor in the leading order term of the "sixth moment of the Riemann zeta function".
It is a pronic number, and the third 15-gonal number. It is a meandric number and an open meandric number.
Since the greatest prime factor of 42 squared + 1 = 1765 is 353 and thus more than 42 twice, 42 is a Stormer Number.
42 is a perfect score on the USA Math Olympiad, and International Math Olympiad.
In base10, 42 is a Harshad Number and a self number, while it is a repdigit in base 4 (as 222).
The eight digits of pi beginning from 242,422 places after the decimal point are 42424242.
Given 27 same-size cubes whose nominal values progress from 1 to 27, a 3x3x3 "magic cube" can be constructed such that every row, column, and corridor, and every diagonal passing through the center, comprises 3 cubes whose sum of values is 42.
In Science
42 is the atomic number of molybdenum.
42 is the angle in degrees for which a rainbow appears.
In 1965, mathmetician Paul Cooper theorized that the fastest, most efficient way to travel across continents would be to bore a straight hollow tube directly through the Earth, connecting a set of antipodes, evacuate it, and then just fall through. The first half of the journey consists of free-fall acceleration, while the second half consists of an exactly equal deceleration. The time for such a journey works out to be 42 minutes. Remarkably, even if the tube does not pass through the exact center of the Earth, the time for a journey powered entirely by gravity always works out to be 42 minutes, as long as the tube remains friction-free, as while gravity's force would be lessened, so would the distance traveled at an equal rate.
The same idea was proposed by Lewis Carroll in Sylvie & Bruno vol.2 chapter7, without calculation.
In Astronomy
Messier object M42, is a magnitude 5.0 diffuse nebula in the constellation Orion, also known as the Orion Nebula.
In the New General Catalogue, object NGC42 is a spiral galaxy in the constellation Pegasus.
In January 2005, Asteroid 2001DA42 was given the name Asteroid Douglasadams in honor of Douglas Adams who popularized the number and died in 2001. Brian Marsden, Director of the Minor Planet Center, and secretary for the naming commitee said, "With even his initials in the provisional designation, this was sort of made for him, wasn't it?"
In Religion
The number 42 appears in various contexts in Christianity. There are 42 generations in Matthew's version of the geneology of Christ.
Revelations 13:5 - It is prophesied that for 42 months the Beast will hold dominion over the Earth.
Ezra 2:24 - 42 men of Beth-azmaveth were counted in the census of men of Israel upon the return from exile.
2Kings 2:23 - God sent bears to maul 42 of the youths who mock Elisha for his baldness.
1Samuel 13:1 - Saul reigned 42 years as king over Israel.
In Ma'at, the ancient Egyptian personification of physical and moral law, order, and truth, there are 42 principals.
In Judaism, there is a 42-lettered name ascribed to God. Rab, a 3rd century source in the Talmud stated, "The Forty-Two Lettered Name is entrusted only to him who is pious, meek, middle-aged, free from bad temper, sober, and not insistent on his rights."
Maimonides felt that the original Talmudic Forty-Two Lettered Name was perhaps composed of several combined divine names. The apparently unpronouncable tetragrammaton provides the backdrop from the Twelve-Lettered Name and the Forty-Lettered Name of the Talmud.
In Kabalistic tradition, 42 is the number with which God creates the Universe.
In Popular Culture
Lewis Carroll's Alice has 42 illustrations, and in Chapter 12, the king explains "the oldest rule in the book. Rule Forty-Two: All persons more than a mile high are to leave the court."
Carroll also uses the number in The Hunting of the Snark, "He had forty-two boxes, all carefully packed . . ."
The first book to be printed with movable type, the Gutenberg Bible, is also known as the "42-Line Bible", after the number of lines of print on each page.
In Property of a Lady from Octopussy, James Bond attends the auction of a Faberge' egg which was Lot number 42.
In Rudyard Kipling's The Travels of Captain Ryalls, Michael Ryalls first enters the jungle at the age of 42. He travels with a 42-inch bull named Regis.
Level 42 - English pop band
"42" is one of the tracks on Coldplay's Viva La Vida, or Death and All His Friends.
42 is one of the Numbers (4, 8, 15, 16, 23, 42) featured in Lost.
42 is the name of a Doctor Who episode set in real time, lasting approximately 42 minutes.
In The X-Files, Fox Mulder lives in apartment number 42.
In Star Trek: The Next Generation, the USS Enterprise NCC-1701-D has 42 decks.
42 is the name of Buzz Lightyear's space ship in Pixar's series Buzz Lightyear of Star Command.
In Notting Hill, the parking space in front of the bookstore is number 42.
In the PC game Spore, reaching the center of the galaxy yields an item known as the Staff of Life, which can be used 42 times.
In Sports
42 is Jackie Robinson's jersey number, and is the only number retired by all MLB teams.
42 is the jersey number of football Hall of Fame star Ronnie Lott, safety for the 49ers. His jersey number was retired in 2003.
42 is the jersey number of Pat Tillman, which was retired by Arizona State University in 2004.
There are 42 Laws of Cricket
42 was the number on Lee Petty's car when he raced in NASCAR.
42 was also the number on Juan Pablo Montoya's race car in the Nascar Sprint Cup Series.
42 is a Texan trick-taking game played with dominoes.
42 is a common "magic number" used by programmers.
In the TIFF image file format, the second 16-bit word of every file is 42.
In the reiser4 file system, 42 is the inode number of the root directory.
In the ASCII character code, and other codes based on it, 42 represents the asterisk character.
In the web search engines Google and Wolfram Alpha, if "the answer to life, the universe, and everything" is entered as a query, the result will be 42.
Here's a few clues as to why that is the case . . .
In Mathmatics
Forty-two is an Abundant Number; its factorization 2x3x7 makes it the second sphenic number and also the second of the form {2x3xr}. As with all numbers of this form, the aliquot sum is abundant by 12. Forty-two is also the second sphenic number to be bracketed by twin primes; 30 also rests between two primes. 42 has a 14 member aliquot sequence: 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0, and is itself part of the aliquot sequence commencing with the first sphenic number, 30.
Further, 42 is the 10th member of the 3-aliquot tree.
Forty-two is the product of the first three terms of Sylvester's Sequence; like the first four such numbers, it is a primary pseudoperfect number.
It is the sum of the totient function for the first eleven integers.
It is a Catalan Number. Consequently, 42 is the number of noncrossing partitions of a set of five elements, the number of triangulations of a heptagon, the number of rooted ordered binary trees with six leaves, and the number of ways in which five pairs of nested parentheses can be arranged.
It is the reciprocal of a Bernoulli Number.
It is conjectured to be the scaling factor in the leading order term of the "sixth moment of the Riemann zeta function".
It is a pronic number, and the third 15-gonal number. It is a meandric number and an open meandric number.
Since the greatest prime factor of 42 squared + 1 = 1765 is 353 and thus more than 42 twice, 42 is a Stormer Number.
42 is a perfect score on the USA Math Olympiad, and International Math Olympiad.
In base10, 42 is a Harshad Number and a self number, while it is a repdigit in base 4 (as 222).
The eight digits of pi beginning from 242,422 places after the decimal point are 42424242.
Given 27 same-size cubes whose nominal values progress from 1 to 27, a 3x3x3 "magic cube" can be constructed such that every row, column, and corridor, and every diagonal passing through the center, comprises 3 cubes whose sum of values is 42.
In Science
42 is the atomic number of molybdenum.
42 is the angle in degrees for which a rainbow appears.
In 1965, mathmetician Paul Cooper theorized that the fastest, most efficient way to travel across continents would be to bore a straight hollow tube directly through the Earth, connecting a set of antipodes, evacuate it, and then just fall through. The first half of the journey consists of free-fall acceleration, while the second half consists of an exactly equal deceleration. The time for such a journey works out to be 42 minutes. Remarkably, even if the tube does not pass through the exact center of the Earth, the time for a journey powered entirely by gravity always works out to be 42 minutes, as long as the tube remains friction-free, as while gravity's force would be lessened, so would the distance traveled at an equal rate.
The same idea was proposed by Lewis Carroll in Sylvie & Bruno vol.2 chapter7, without calculation.
In Astronomy
Messier object M42, is a magnitude 5.0 diffuse nebula in the constellation Orion, also known as the Orion Nebula.
In the New General Catalogue, object NGC42 is a spiral galaxy in the constellation Pegasus.
In January 2005, Asteroid 2001DA42 was given the name Asteroid Douglasadams in honor of Douglas Adams who popularized the number and died in 2001. Brian Marsden, Director of the Minor Planet Center, and secretary for the naming commitee said, "With even his initials in the provisional designation, this was sort of made for him, wasn't it?"
In Religion
The number 42 appears in various contexts in Christianity. There are 42 generations in Matthew's version of the geneology of Christ.
Revelations 13:5 - It is prophesied that for 42 months the Beast will hold dominion over the Earth.
Ezra 2:24 - 42 men of Beth-azmaveth were counted in the census of men of Israel upon the return from exile.
2Kings 2:23 - God sent bears to maul 42 of the youths who mock Elisha for his baldness.
1Samuel 13:1 - Saul reigned 42 years as king over Israel.
In Ma'at, the ancient Egyptian personification of physical and moral law, order, and truth, there are 42 principals.
In Judaism, there is a 42-lettered name ascribed to God. Rab, a 3rd century source in the Talmud stated, "The Forty-Two Lettered Name is entrusted only to him who is pious, meek, middle-aged, free from bad temper, sober, and not insistent on his rights."
Maimonides felt that the original Talmudic Forty-Two Lettered Name was perhaps composed of several combined divine names. The apparently unpronouncable tetragrammaton provides the backdrop from the Twelve-Lettered Name and the Forty-Lettered Name of the Talmud.
In Kabalistic tradition, 42 is the number with which God creates the Universe.
In Popular Culture
Lewis Carroll's Alice has 42 illustrations, and in Chapter 12, the king explains "the oldest rule in the book. Rule Forty-Two: All persons more than a mile high are to leave the court."
Carroll also uses the number in The Hunting of the Snark, "He had forty-two boxes, all carefully packed . . ."
The first book to be printed with movable type, the Gutenberg Bible, is also known as the "42-Line Bible", after the number of lines of print on each page.
In Property of a Lady from Octopussy, James Bond attends the auction of a Faberge' egg which was Lot number 42.
In Rudyard Kipling's The Travels of Captain Ryalls, Michael Ryalls first enters the jungle at the age of 42. He travels with a 42-inch bull named Regis.
Level 42 - English pop band
"42" is one of the tracks on Coldplay's Viva La Vida, or Death and All His Friends.
42 is one of the Numbers (4, 8, 15, 16, 23, 42) featured in Lost.
42 is the name of a Doctor Who episode set in real time, lasting approximately 42 minutes.
In The X-Files, Fox Mulder lives in apartment number 42.
In Star Trek: The Next Generation, the USS Enterprise NCC-1701-D has 42 decks.
42 is the name of Buzz Lightyear's space ship in Pixar's series Buzz Lightyear of Star Command.
In Notting Hill, the parking space in front of the bookstore is number 42.
In the PC game Spore, reaching the center of the galaxy yields an item known as the Staff of Life, which can be used 42 times.
In Sports
42 is Jackie Robinson's jersey number, and is the only number retired by all MLB teams.
42 is the jersey number of football Hall of Fame star Ronnie Lott, safety for the 49ers. His jersey number was retired in 2003.
42 is the jersey number of Pat Tillman, which was retired by Arizona State University in 2004.
There are 42 Laws of Cricket
42 was the number on Lee Petty's car when he raced in NASCAR.
42 was also the number on Juan Pablo Montoya's race car in the Nascar Sprint Cup Series.
In Other Fields
In the City of London, the former NatWest Tower, is known as Tower42.
42 is a Texan trick-taking game played with dominoes.
42 is a common "magic number" used by programmers.
In the TIFF image file format, the second 16-bit word of every file is 42.
In the reiser4 file system, 42 is the inode number of the root directory.
In the ASCII character code, and other codes based on it, 42 represents the asterisk character.
In the web search engines Google and Wolfram Alpha, if "the answer to life, the universe, and everything" is entered as a query, the result will be 42.
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